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Maple for Windows
Bert G. Wachsmuth
In 1959 at MIT a group of researchers developed a system called MACSYMA, the first computer algebra system. That system was intended partially to convince the science community that computers could perform significant intellectual tasks. The system could manipulate symbols as well as numbers, and was useful for tasks for which computers could not be used before. Since then several other computer algebra systems were developed, with different underlying philosophies. Three such systems have proved especially useful: Mathematica, Maple, and Derive. Mathematica is the Cadilac of computer algebra systems: it is expensive, uses a lot of system resources, but delivers superb performance. Maple is the VW of computer algebra systems: it is affordable and sturdy, cheap on system resorces, delivers adequate performance, but lacks an aura of grandeur. Derive is the car for the non-driver: it has all the features of a real car, but it assists you in handling the controls whenever possible and in doing so may occasionally restrict your creativity to avoid mistakes.
To use Maple for Windows it helps to be familiar with Microsoft Windows. When you start Maple, you will see its main window on the screen and after a seconds Maple will be ready for your input. On top of the main window you will find a menu bar which offers several choices. You might want to see what each menu item has to offer before starting to use Maple. Three things should be kept in mind at all times:
 | Maple has an extremly good help facility, as well as a ‘Help Browser’:
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| Every command in Maple must by typed in, according to some syntax rules. Use the help facilities to find out the exact form of each command and its options | ||||
| Every command in Maple must end with a semicolon. If you forget to enter a semicolon, no computation will happen. However, you can simply type a semicolon on the next line by itself to start the computation |
A Brief Maple Session
Start Maple and type the lines on the left. Maple should act in the way indicated. Remember, Maple is a Windows program so you can use the familiar window resizing commands, cut-and-paste, scrolling, etc.
| help(intro); | Displays an introductory help message about Maple |
| 123 - 5/2 * (44/7 - 99/2)^2; | add fractions and numbers |
| evalf(%); | gives a float-point (decimal) approximation of last result. The single percent stand for the ‘last computed expression’ |
| evalf(Pi,100); | show decimal approximation of Pi to 100 decimals |
| P := x -> x^2 - x - 6; | defines a function P(x) |
| P(sqrt(2)); | evaluates P at root(2) |
| factor(P(x)); | factors P(x) over the rationals |
| expand(%); | expands a factored expression |
| solve(P(x)=0,x); | solve the equation P(x) = 0 for x |
| plot(P(x),x=-5..5) | plots polynomial for x in [-5,5] |
| f := x -> x^3 - 2*x; | defines a function f(x) |
| plot({P(x),f(x)},x=-5..5); | plots P(x) and f(x) in one coordinate system |
Here is a short list of useful Maple functions. Use the help facility to find out more about each command.
Essential Commands
| diff | find derivatives | plot | create a two-dimensional plot of an expression |
| evalf | evaluate an expression | simplify | simplify an expression |
| int | integrate expressions (definite /indefinite integral) | solve | solve an equation or system of equations |
| limit | calculate the limiting value of an expression | subs | substitute one expression into another |
| % | single percent stand for last computed expression | %% | double percent stand for second-to-last computed expression |
More Commands
| assume | make assumptions such a a variable being positive | normal | normalize a rational expression |
| convert | convert an expression to a different form | numer | extracts numerator of fraction |
| denom | extracts denominator of fraction | rhs, lhs | extract right-hand-side or left-hand-side of an equations |
| expand | simplify an expression by distribution law | seq | generates a sequence according to some rule |
| factor | factor a polynomial | sum | finds the sum of expressions |
| fsolve | find approximate solutions |
Functions
| abs(x) | absolute value | exp(x), E^x | exponential function |
| sin(x), cos(x), tan(x) | trig. Functions | log(x), ln(x) | natural logarithm |
| sqrt(x) | square root function | arctan(x), arcsin(x), arccos(x) | inverse trig. Functions |
Constants
| Pi | constant Pi = 3.1415 | infinity | positive infinity |
| E or exp(1) | exponential number e = 2.7182 |
Simple Programming
| defining simple functions | fname := x -> expression; |
iterations | for i from 1 by 2 to 10 do expression; od; |
| defining general functions | fname := proc(x) expression1; expression2; ...; end; |
conditional evaluation | if condition1 then statement else statement fi; |
There are several nice booklets available which explain Maple with a student's viewpoint in mind. One such booklet is usually provided when you purchase the Student Edition of Maple. Another very nice book is Maple V: First Leaves' by B.W. Char and others, Springer Verlag 1992.
| Some sample problems using Maple |